Question

Find the direction cosines of the following vectors:
\[6 \hat{i} - 2 \hat{j} - 3 \hat{k}\]

 

Answer 1

We have,
\[6 \hat{i} - 2 \hat{j} - 3 \hat{k}\]
The direction cosines are \[\frac{6}{\sqrt{6^2 + \left( - 2 \right)^2 + \left( - 3 \right)^2}} , \frac{- 2}{\sqrt{6^2 + \left( - 2 \right)^2 + \left( - 3 \right)^2}} , \frac{- 3}{\sqrt{6^2 + \left( - 2 \right)^2 + \left( - 3 \right)^2}}\]  or,  
\[\frac{6}{7}, \frac{- 2}{7}, \frac{- 3}{7}\]